Question

The rank of the matrix \(\begin{bmatrix} 1 & 1 & 1 \\\ a & b & c \\\ a^2 & b^2 & c^2 \end{bmatrix}\) where a = b ≠ c is:

Answer 1

Correct Answer - Option 3 : 2

Concept:

The number of non-zero rows or columns defined as the rank of the matrix.

Given:  

a = b ≠ c 

Calculation:

e =  \(\begin{bmatrix} 1 & 1 & 1 \\\ a & b & c \\\ a^2 & b^2 & c^2 \end{bmatrix}\)

Put b = a in the above matrix

e = \(\begin{bmatrix} 1 & 1 & 1 \\\ a & a & c \\\ a^2 & a^2 & c^2 \end{bmatrix}\)

Perform C₁ = C₁ - C₂

e = \(\begin{bmatrix} 0 & 1 & 1 \\\ 0 & a & c \\\ 0 & a^2 & c^2 \end{bmatrix}\)

So from the above number of non-zero columns = 2

Hence, Rank of the matrix = 2